In this paper, we show that the PBH binaries can be detected by the high redshift \(z > 20\)  gravitational wave signals. During the propagation of gravitational wave from high redshift to the present, the frequency of gravitational wave is decreasing so that lies in the frequency band of gravitational wave detectors. Then amplitude of redshifted high frequency gravitational wave can significantly enhance the \(\mathrm {S/N}\)  at \(z > z_{\mathrm {min}}\) , where \(z_{\mathrm {min}} = 2.63\)  in \(\Lambda \mathrm {CDM}\)  model. This phenomena is detailed studied in [1]}. In order to detect gravitational wave signal from PBH binaries within practical observation time. The event rate of gravitational wave from PBH binaries is estimated. We consider the model in [2]}, the PBH binaries events are enhanced at high redshift which can achieve \(90 \mathrm {cGpc}^{-3}\mathrm {yr}^{-1}\)  at \(z = 20\)  for PBHs mass 100 solar masses with \(f_{\mathrm {PBH}} = 10^{-3}\)  in Fig. REF . The enhancement of gravitational wave signals and the event rate from PBH binaries at high redshift improve the detectability of PBH binaries. Then, we study the effect of initial clustering of PBHs on its detectability as we have studied in [3]}. An enhancement in effectively detectable mass ranges appears by the initial clustering of PBHs. The effectively observable mass range covers \(20 - 10^{3}\)  solar masses at \(z = 20\)  within ten years observation time on LISA. This mass range can be enhanced to \(20 - 10^6\)  solar masses with initial clustering \(\beta = 10^{-4}\) . The wide mass range shows that it is possible to detect the PBH binaries on LISA and SKA at high redshift.
